Mr. Omidyar, the founder of eBay, wants to build a dairy farm on the island of Kauai.

He is one of many tech billionaires who have established a presence in Hawaii, which is only a five-hour flight from Silicon Valley. Others include Larry Ellison, Oracle’s co-founder, who bought all but a tiny amount of the island of Lanai and turned it into a resort — investing millions, but frustrating some islanders by driving up rents — and Facebook’s Mark Zuckerberg, who was called a “neocolonialist” after he sued some locals over beachfront land he bought. (He dropped the suits.)

The goal of Mr. Omidyar’s farm — which incidentally is on land owned by the family of Steve Case, another tech billionaire — is to decrease the island-state’s heavy reliance on imported milk, while using sustainable agriculture practices. (The dairy will nonetheless still have to import feed for its animals.)

Some residents, though, object. They and the owners of the major resorts that line this island’s famous beaches, just a little over one mile down the coastline from the dairy site, have worked to block the project.

“We are concerned with odors and flies from the dairy,” said Lisa Munger, a lawyer who represents the Grand Hyatt Kauai Resort & Spa, which successfully sued to force the dairy to do an environmental assessment. “Each dairy cow will produce 90.8 pounds of manure per day — whether there are 699 cows or 2,000 cows, that is a lot of manure.”

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Pierre OmidyarCreditMichael Lewis

Ms. Munger said biting flies can reach the Grand Hyatt, along with “offensive dairy odors.”

Opponents of the Hawaii Dairy drive around with bumper stickers — “No Moo Poo in Maha’ulepu,” as the area of the island where the dairy would go is known — summarizing their main cause of concern: that animal waste could contaminate drinking water or the oceanfront and cause unpleasant smells. “We’re all for local agriculture, but why put a dairy there?” said Bridget Hammerquist, a lawyer and the president of Friends of Maha’ulepu, a nonprofit set up to fight the dairy. “It’s a serious threat to Kauai’s biggest source of revenue, tourism, to the environment and to our quality of life.”

So far, courts have sided with opponents of the dairy. In a case brought by the Friends group, contending that the dairy would violate the federal Clean Water Act, a judge ruled that it had violated the law by failing to get the permits it needed for the construction it had already done on the site.

Another lawsuit, brought by the owners of the Grand Hyatt, contended the dairy would have a negative effect on businesses and resorts along the coast. This year, Judge Randal G. B. Valenciano revoked all permits that had been granted to Hawaii Dairy Farms and ordered it to complete an environmental assessment before going further.

Amy Hennessey, director of communications at the Ulupono Initiative, Mr. Omidyar’s investment office in Hawaii, said those decisions were a setback for Hawaiian agriculture and food security, which has been a concern of Gov. David Y. Ige. Hawaii imports roughly 90 percent of its food supply, and Mr. Ige has pledged to double the state’s food production by 2020.

“We’ve gone from an economy here that grew sugar cane and pineapples and had a large agricultural industry to one based largely on tourism and real estate development,” Ms. Hennessey said. “All these interests are competing for the same resources and opportunities, and if we’re not careful, agriculture is going to lose out and Hawaii will be without a safety net — not being able to grow our own food is a significant issue.”

Residents point out that one drinking-water well supplying the neighborhoods of Poipu and Koloa is within 700 feet of the pastures where the cows will graze, and other wells are within 1,200 feet.

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Amy Hennessey, a spokeswoman for the Ulupono Initiative, explains how different grasses planted on the proposed dairy farm will help absorb manure.CreditMarco Garcia for The New York Times

The dairy’s representatives contend that the soil at the site can absorb and filter the manure runoff from 699 milk cows.The chosen number of cows is significant: If Hawaii Dairy’s plans included one more cow — bumping the total to 700 — it would meet the Environmental Protection Agency’s definition of a “large concentrated animal feeding operation,” or CAFO.

That designation initiates the need for a permit under the Environmental Protection Agency’s Pollutant Discharge Elimination System. Because the dairy drew the line at 699 cows, avoiding the need for the discharge permit, it originally was able to describe itself as “zero discharge.”

“It’s going to be zero discharge from the E.P.A.’s perspective,” Ms. Hennessey said. “There will be very little discharge, but I think it was a little confusing for some people in the community, so we’ve stopped saying that,” she said.

The dairy plans to eventually have 2,000 cows on the property.

Given Hawaii’s proximity to Silicon Valley, it is little surprise that the islands have attracted many of America’s new billionaires. Like everyone else, they appreciate the state’s natural beauty. And they appreciate its generally laid-back approach to fame and fortune.

Plus, it is easier to move around by boat and helicopter — avoiding paparazzi stakeouts. Marc Benioff, Paul Allen and Michael Dell, whose 18,500-square-foot hideaway there is known as the Raptor Residence, have homes here.

Mr. Ellison reportedly spent $450 million to renovate a resort on Lanai, one of the smallest of the Hawaiian archipelago’s eight main islands. That resort has the world’s most expensive room, at $21,000 a night, according to Bloomberg. Mr. Ellison is now spending more to renovate another resort.

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Poipu Beach in Hawaii. The proposed dairy farm in the area has been met with resistance from local residents, who say runoff from the farm will harm the environment and drive tourists away.CreditMarco Garcia for The New York Times

While his improvements have driven up rents, displacing some residents — only about 3,200 people live there full time — Mr. Ellison has also paid for a new water filtration system for the island, a public pool and a movie theater.

Mr. Zuckerberg and his wife, Priscilla Chan, are the latest of the tech titans to establish a toehold here, buying 700 acres on Kauai for a reported $100 million. In January, after public outcry, they dropped eight lawsuits they had brought against dozens of people who have claims to parcels of land within their estate dating back to the mid-1800s.

The suits touched on a particularly sensitive issue for native Hawaiians having to do with land that traditionally belonged to Hawaii’s kings. Mr. Zuckerberg and Dr. Chan said in a letter printed in the local newspaper that they had been unaware of some of the issues involving such parcels and pledged to learn more.

The Omidyars have lived in Honolulu more or less full time since the mid-2000s, and it is not the eBay billionaire’s first run-in with the Kauai community. He previously planned to open a resort on the island’s north shore on a property that was home to a Club Med. But he had to give up after about a tenth of the island’s population signed a petition against the project, claiming its impact on the environment would be detrimental.

He lived in Hawaii for two years when he was a teenager, and his wife, Pam, attended ’Iolani School in Honolulu. Today, he tends to keep a low profile. The couple has a private security staff that includes former Secret Service and State Department officers, and they keep a private plane at the ready at Honolulu Airport, which Mr. Omidyar has said is so that the family can escape a disaster quickly.

He has also devoted $250 million to building a media business that includes online publications like The Intercept and Civil Beat, based in Honolulu, which tend to keep a weather eye on government and its secrets.

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An aerial view of Maha’ulepu Beach. Opponents of the Hawaii Dairy drive around with bumper stickers — “No Moo Poo in Maha’ulepu.”CreditMarco Garcia for The New York Times

The very isolation he and other billionaires prize is also the cause of one of Mr. Omidyar’s biggest concerns about the state — its need to import most of the food it consumes. That, in turn, explains his interest in setting up a dairy. In a rare interview with The Honolulu Advertiser in 2009, Mr. Omidyar noted that Hawaii had enough food to go without imports for just 11 days.

Hawaii has at least three commercial dairies already — and making money is “an uphill battle,” said Steve Whitesides, the owner of one of them, Big Island Dairy. Permits are hard to get, expenses are high and he has had to import more feed than he expected, he said. Mr. Whitesides, an Idaho-based dairy farmer, bought Big Island Dairy in 2012, when it was flirting with bankruptcy.

Recently, the state department of health fined Big Island Dairy $25,000 for illegally allowing animal waste to flow into local water supplies. The tiny town of O’okala sits below the 2,500 acre Big Island Dairy, and its residents had long complained to the state about bad smells and wastewater in the gulches and waterways that run through their yards and streets on the way to the ocean.

Last September, heavy rains led to flooding in O’okala, and some residents found themselves up to their ankles in wastewater carried down the mountain. They posted videos to YouTube documenting the experience and wrote letters to state officials. “Older people have told me they have a hard time eating dinner because of the smell, and homeowners have gotten E. coli and staph infections,” said Valerie Poindexter, who represents the neighborhood on the Hawai’i County Council.

Mr. Whitesides said Big Island Dairy was built to “proper specs” and that he had continued to invest in its infrastructure to improve it. He said he did not believe manure was escaping from the two effluent ponds on the property, or the milking building. But the dairy does have some animals in pastures, he said, “And that manure has to go somewhere.”

To avoid any problems like that at Mr. Omidyar’s dairy, Ms. Hennessey said, Hawaii Dairy will establish 35-foot setbacks, planted with dense vegetation, along a stream that runs through the property to prevent contamination of the waterway running through the property to the sea. The company also plans to introduce dung beetles to the property, Hawaii Dairy said, to help process manure.

The dairy has submitted a final environmental statement to state health authorities and is waiting for their response to decide how to proceed, Ms. Hennessey said.

Correction:

An earlier version of this article referred incorrectly to Lanai. At least two of the Hawaiian archipelago’s eight main islands — Niihau and Kahoolawe — are smaller, along with many other islands and atolls in the chain; it is not the smallest Hawaiian island.

A version of this article appears in print on , on Page B1 of the New York edition with the headline: Paradise for a Tech Billionaire? Sun, Sand … And 699 Cows. Order Reprints | Today’s Paper | Subscribe

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